The present invention relates to an improved bioreactor apparatus useful for eukaryotic cell culture, where cell density and bioproduct are increased by, using a molecular weight cutoff filter. The apparatus of the present invention utilizes design features which afford optimum agitation of the cells with minimum mechanical shear force. This is accomplished by utilizing a gas feed to provide gentle aeration and mixing. The novel feature of the invention is the use of an external molecular weight cutoff (MWCO) filter to perfuse nutrients in and waste products out of the bioreactor while maintaining cells and their products within the bioreactor.